Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to approximate f(1.02, -1.97) without a calculator.

Q: Estimate f(2.98, –1.99) given that f(3, –2) = 2, f«(3, –2) -3 and fy(3, –2) = -4. = f(2.98, –1.99)

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Q: -22 - x2, find f(x), f(x), f(x), and f(4)(x). " (x) 70 = aph f, f', f", and f" on a common screen. y…

A: Given query is to find indicated derivatives.

Q: 1+х f[X_, Y_] := 2 у - 1-x (1+) (у-1)2

A: We will use basic knowledge of the functions of several variable theory to answer this question.  We…

Q: (S dx (f(+ 2t)° dt (2+3x)

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Q: Given f"(x) = 6x - 5 and f'(-3) = -1 and f(-3) = -2. Find f'(x) = and find f(4) = %3D

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Q: What is the solution for solving for +y?

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Q: v=(*++1)(r+2) 11. (u)=(1+ \u)(u-u°)

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Differentiate the function f(t) = t^3 − it^2 when t = 2

A: Here, f(t)=t3-it2⇒f'(t)=3t2-i(2t)⇒f'(t)=3t2-2ti

Q: Is this function analytic fizz=. (1 +x)? +y2 2

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Q: x²y" + 3ry – 24y = 0, y(1) = -8, y'(1) = –7. y =

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Q: Find f. f "(x) = x-2, x > 0, f(1) = 0, f(5) = 0 f(x) =

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Q: Differentiate the function. h(t) = √t-8e* h'(t)

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Q: Use the First Derivative Test to find the relative extrema of ƒ(x)=· sin x on (0,27).

A: The given function is- fx=x2-sinx  Differentiating f(x) w.r.t x- f'x=12-cosx Put f'x=0,…

Q: differe ntiato a) f(x) =10ge (X)x (3x)3 lincx))

A: Solution -  a.) Given function -  f(x)=log2(x) × (3x)3  We can write it as -…

Q: Find all complementary functions of the equation xy" - 2y'=0, x>0 1, x² x₁ x³ a. b. C. d. x, x(Inx)²…

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Q: Find the second derivative (y") of the given function: 6. y 2-e -6e* +12e-e" (2-e*)" 6e* (2+e*)…

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Q: Calculate y" for the function y = 5x' – 7x² +16

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Q: The following quadratic function is given: f(t) = 5t²-7t + 25. i) ii) Use first principle to find…

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Q: Suppose f(x)=x^4+3x+1 on the interval [−4,−1]. Find x when f′(x)=0.

A: Given function is Differentiating with respect to x , we get

Q: f(x,y)=x^4+y^4-4xy Find all the endpoints of the function.

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Q: Find f. f "(x) x2, x > 0, f(1) 0, f(9) 0 =

A: Given,